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arXiv · hep-th/9606144

Faces of Relativistic Toda Chain

S. Kharchev·A. Mironov·A. Zhedanov
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Abstract

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and, which is the same, to the two-component Volterra hierarchy while its forced (semi-infinite) variant is described by the unitary matrix integral. The integrable properties of the RTC hierarchy are revealed in different frameworks of: Lax representation, orthogonal polynomial systems, and $τ$-function approach. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. Some applications to biorthogonal polynomial systems are discussed.

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S. Kharchev, A. Mironov, A. Zhedanov. 1996-12-05. Faces of Relativistic Toda Chain. https://doi.org/10.1142/s0217751x97001493

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